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Math Help - Help with local max/min and global max/min

  1. #1
    Junior Member
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    Help with local max/min and global max/min

    I know how to solve for local min and max.

    For instance,

    F = 2x^2 + y^2 +4x -4y +5

    The point (-1,2) is a local minimum, but my book also points out that it is a global minimum.

    Can anyone tell me how to find the global max/min after I have found critical points and local max/min.
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  2. #2
    Senior Member apcalculus's Avatar
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    A global min is a point where the y-value is the least of all possible y-values in the range of the function. No other output will be less.
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  3. #3
    Super Member Matt Westwood's Avatar
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    Quote Originally Posted by messianic View Post
    I know how to solve for local min and max.

    For instance,

    F = 2x^2 + y^2 +4x -4y +5

    The point (-1,2) is a local minimum, but my book also points out that it is a global minimum.

    Can anyone tell me how to find the global max/min after I have found critical points and local max/min.
    If you have found all the local minima, then (assuming the function doesn't go off to - \infty at any point), the global minimum is the smallest of the local minima.

    So what you need to do, to prove a global minimum, is show that it's the smallest of the local minima, and that the curve does not go off to - \infty.

    Yes I know you weren't told to prove that it is a global minimum, consider this post a "for information" one.
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